3t2=t+6

Solution for 3t2=t+6 equation:

3t^2=t+6

We move all terms to the left:

3t^2-(t+6)=0

We get rid of parentheses

3t^2-t-6=0

We add all the numbers together, and all the variables

3t^2-1t-6=0

a = 3; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·3·(-6)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{73}}{2*3}=\frac{1-\sqrt{73}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{73}}{2*3}=\frac{1+\sqrt{73}}{6}
$